我明天去纽约。 sounds more natural to me. If you say this sentence, I guess it's sure, you are already preparing to go to New York, and already have the ticket. Probably that's why you use the present continuous in English. (At least what they taught me about English)

会 has more an idea of future planning, usually farther future, which in English you will probably use "will" or "be going to".

I can't explain the difference with or without 的。I fell that with 的 it sounds more like a promise, without 的 sounds more like a planning.

Oh? I wasn't aware that 會 was used to express uncertainty.. I've always used it to convey "going to" or "will", as described in post #3 above. It just doesn't seem to fit in the present context, though it'd be great in a different one:

The use of 会 is often to indicate that the event is not 100% certainty (ie, not yet a fact). For this reason, you often see 的 is added 会 in assertions, to increase the certainly (which is usually to convince people of the certainty for the very reason that it's not a certainty ).

Do future constructions with 会 always need a 的 at the end? (will they always seem incomplete without it?)

For example:
(I'm going to New York tomorrow)
我明天会去纽约的.

I often will omit the 的. Is it better if it is included? (or is there a difference between a future construction with or without "的"?)

Thanks/谢谢！

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Although leaving 的 could be ok, having it will make the sentence more natural.
的 has two functions here:
1. As a reconfirmaton.
2. To avoid the sentence becomes too short. Chinese don't like very short sentences. So 我会想你 sounds not very good, but 我明天会去纽约 is totally ok.